The present invention relates generally to the field of cranes. More specifically, the present invention relates to methods of and apparatuses for controlling residual oscillation associated with the movement of suspended payloads of rotary-style cranes.
In general, construction, transportation, and other cranes can be grouped into one of two categories based on their configuration: gantry-style cranes and rotary-style cranes.
The first category is gantry-style crane systems, which incorporate a trolley that translates in a horizontal plane. Attached to the trolley is a load-line for payload attachment. Typically, gantry-style crane systems have varying load-line length capabilities. Gantry-style cranes exhibit a one degree-of-freedom sway (one direction).
The second category is rotary or jib crane systems, for which the load-line attachment point undergoes rotation. A rotary crane includes a pendulum-like end line attached to a rotatable jib. Within this general category of cranes, there exist devices with multiple degrees-of-freedom including variable (adjustable) load-line length and variable jib length. Other degrees-of-freedom may exist such as translation of the load-line attachment point along the jib, or if the jib is replaced by a boom, the characteristic boom rotational motion. Boom rotational motion, referred to as luffing, causes the tip of the boom to move vertically. Conventionally, point-to-point payload maneuvers using jib cranes are performed so as not to excite the spherical pendulum modes (revolute motion) of their cable and payload assemblies. Typically, these spherical pendulum modes, although time-varying, exhibit low frequencies. The first principal motion of the payload resulting from the point-to-point maneuver is a sway tangential to the arc traced by the tip of the jib. The second principal motion of the payload resulting from the point-to-point maneuver is a sway radially from the point of rotation caused by the centripetal acceleration of the payload. At the end of a nominal point-to-point maneuver, the payload oscillates in these two directions. The resulting maneuvers are therefore performed slowly, contributing to high construction and transportation costs.
During crane transport, a payload is free to swing in a spherical pendulum-like motion. If the payload oscillates during crane transportation, then the oscillation must be damped sufficiently by the crane operator or be allowed to decay naturally before the next operation begins. Either option is costly, time consuming, and reduces facility availability. If the crane system can be automated with a programmable computer, however, oscillation of the payload can be eliminated by reacting to the forces created by the spherical pendulum-like motion associated with movement of the payload. In addition, programmability allows movement of suspended objects that are initially at rest without introduction of payload oscillation. Thus, cost, time, facility, and other requirements can be minimized.
Currently, most industrial cranes do not automatically compensate for suspended payload swing at the end of a motion. The crane operator relies on experience to bring the payload to a swing-free stop. Failure of the operator to successfully stop the payload from swinging causes a decrease in operating efficiency. Similarly, a container cannot be safely placed at a stationary position if the payload is moving.
Unfortunately, cranes are used most often in unstructured environments, such as in ship yards and factory floors, where the end position in crane coordinates is not well specified. For example, the desired position of a payload on a ship is not well specified because placement of payloads on ships is not uniform. Therefore, most cranes are guided to their final destination by an operator with the aid of an operator input device, such as a joystick.
Those industrial cranes that automatically compensate for suspended payload swing at the end of a motion typically work only for pre-planned motions where the desired start and end positions of the payload in crane coordinates are well specified. The acceleration and constant velocity times of the motion profiles are planned so that they are a function of the natural period of oscillation .tau. of the pendulum-like motion associated with movement of the payload; the period of oscillation .tau. is characterized by ##EQU1## where g is gravity, L is the cable length, and .omega. is the natural frequency of oscillation of the suspended payload.
The field is replete with crane control systems that attempt to eliminate payload swing. Examples of some swing-free crane-related patents are the following:
U.S. Pat. No. 5,443,566, Electronic Antisway Control, of Rushmer et al. depicts a system for the electronic control of the sway of a suspended load from a crane. The natural frequency .omega..sub.n of a simple pendulum is used to estimate the velocity and displacement of the suspended load, and a signal representative of measured load displacement is used to drive the estimated load displacement to the measured load displacement and modify the estimated velocity.
U.S. Pat. No. 5,219,420, Procedure for the Control of a Crane, of Kiiski et al. depicts a method for damping the swing of the load of a crane during a traversing motion of the trolley and/or bridge when the trolley bridge is controlled by a signal that controls the traversing motor. The length of the hoisting rope is determined and used for the calculation of the time of oscillation of the load swing, and when a new speed setting is given, a first control signal compensating the swing prevailing at the moment and a second control signal changing the speed are generated.
U.S. Pat. No. 5,127,533, Method of Damping the Sway of the Load of a Crane, of Virkkunen depicts a system for damping the sway of the load moved by the carriage of the crane, the load being suspended by at least one hoisting rope. The damping is achieved by using a discrete time-domain control system whose control interval is varied in accordance with the hoisting rope length while the control parameters remain constant. The system depicts the use of a transfer function in the formulation of the control and a discrete time-domain control; all transfer functions presented by Virkkunen are formulated using continuous time-domain notation. Virkkunen's system uses fixed-parameter control with a variable control interval. Virkkunen starts with a nominal control interval of 100-ms and modifies the control interval based on the cable length. As depicted in FIG. 3 of Virkkunen, the control method requires a measurement of the carriage position x.sub.T, cable sway .phi., and cable length L. Equation 2 of Virkkunen is then applied to solve for the reference speed r.sub.T.
U.S. Pat. No. 4,997,095, Methods of and System for Swing Damping Movement of Suspended Objects, of Jones et al. (including B. Petterson, co-inventor named in the present application) depicts methods of and system for damping a payload suspended from a gantry-style crane in accordance with a control algorithm based on the periodic motion of the suspended mass or by servoing on the forces induced by the suspended mass.
U.S. Pat. No. 4,916,635, Shaping Command Inputs to Minimize Unwanted Dynamics, of Singer et al. depicts a system where a sequence of impulses is determined which eliminates unwanted dynamics in the dynamic system. The impulse sequence is convolved with an arbitrary command input to drive the dynamic system to an output with a minimum of unwanted dynamics. The input signal is processed to counteract the effects of unwanted dynamics such as payload swing.
U.S. Pat. No. 4,756,432, Crane Control Method, of Kawashima et al. depicts a crane control method where a payload is moved at a predetermined velocity to a predetermined point by computer control to minimize swinging. Their invention is directed toward a two-pulse method in which mid-course constant velocity is somehow controlled. The control is performed in an accelerating period, a constant velocity travel, and a decelerating period separately, wherein the control is performed during the accelerating and decelerating periods by turning on and off predetermined accelerating and decelerating forces.
U.S. Pat. No. 4,717,029, Crane Control Method, of Yasunobu et al. depicts a method in which a payload suspended by a rope is laterally transported by a trolley, the accelerating and decelerating time of the trolley are obtained on the basis of the mass of the trolley, the mass of the suspended payload, and the rope length. During the constant speed running, the stop position of the trolley is predicted on the basis of the decelerating time.
U.S. Pat. No. 4,603,783, Device on Hoisting Machinery for Automatic Control of the Movement of the Load Carrier, of Tax et al. depicts an automatic control system for controlling the movement of a load and for steadying the associated pendulum-like motion of the load. The system includes a signal transmitter for sending signals for controlling the movement of a load carrier traction motor.
U.S. Pat. No. 4,512,711, Unloading of Goods, Such as Bulk Goods from a Driven, Suspended Load-Carrier, of Ling et al. depicts a method for controlling the lateral displacement of a trolley supporting goods to be unloaded at a certain location. A pendulum is held at a constant angle while the system decelerates to a stop and then accelerates in an opposite direction. The Ling et al. invention does not teach a continuum of solutions and does not use a coupled and nonlinear model.
U.S. Pat. No. 3,921,818, Crane Suspension Control Apparatus, of Yamagishi depicts a system where a crane is accelerated and decelerated with two pulses, the second pulse being timed to counteract the swing of the payload.
U.S. Pat. No. 3,517,830, Cranes, of Virkkala depicts an arrangement for reducing the oscillations of the pendulum-like motion associated with movement of the load. A moving mechanism is provided with a synchronizing device, automatically functioning so that each change of acceleration is automatically succeeded by another equally great and similarly directed change of acceleration after a time, which is half the length of the period of oscillation of the load.
In recent years, many researchers have worked on the control of flexible structures, such as cranes. To date, a general solution to the controls problem has yet to be realized. One very important reason for this is that computationally-efficient mathematical methods do not exist for solving the extremely complex sets of partial differential equations and the associated boundary conditions that most accurately model gantry-style structures. While general solutions do not exist, some interesting solutions do exist for simplified cases. (See, for example, N. C. Singer, Residual Vibration Reduction in Computer Controlled Machines, Technical Report Al-TR 1030, MIT Artificial Intelligence Laboratory, Cambridge, Mass., (January 1989); A. D. Christian, Design and Implementation of a Flexible Robot, Technical Report Al-TR 1153, MIT Artificial Intelligence Laboratory, Cambridge, Mass. (August 1989); Stephen Yurkovich, Anthony P. Tzes, lewen Lee, and Kenneth L. Hillsley, Control,and System Identification of a Two-Link Flexible Manipulator, Proceedings of the 1990 IEEE International Conference on Robotics and Automation, Cincinnati, Ohio, pp. 1626-1631, (May 13-19, 1990); Brett R. Murphy and Ichiro Watanabe, Digital Shaping Filters for Reducing Machine Vibration, IEEE Transactions on Robotics and Automation, vol. 8, no. 2, pp. 285-289 (April 1992); Farshad Khorrami, Analysis of Multi-link Flexible Manipulators Via Asymptotic Expansions, Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, Fla., pp. 2089-2094 (December 1989); and Eduardo Bayo, Philip Papadopoulos, James Stubbe, and Miguel Angel Serna, Inverse Dynamics and Kinematics of Multi-Link Elastic Robots: An Iterative Frequency Domain Approach, The International Journal of Robotics Research, Vol. 8, No. 6, pp. 49-62 (December 1989).).
A simple input-shaping filter that modifies the reference input so that the residual vibrations of Linear Time Invariant ("LTI") systems are eliminated was taught in N. C. Singer, Residual Vibration Reduction in Computer Controlled Machines, Technical Report Al-TR 1030, MIT Artificial Intelligence Laboratory, Cambridge, Mass., (January 1989). N. C. Singer's method involves convolving an input signal with a train of impulses that are calculated based on perfect knowledge of the crane system's flexible mode parameters. When these impulses are convolved with an arbitrary input, the crane system follows the input without vibration and with a time delay approximately equal to the length of the impulse train (typically equal to the period of vibration). This simplification has proven to provide reasonable response when applied to a three-degree-of-freedom flexible robot arm A. D. Christian, Design and Implementation of a Flexible Robot, Technical Report Al-TR 1153, MIT Artificial Intelligence Laboratory, Cambridge, Mass. (August 1989)!. B. R. Murphy and I. Watanabe later extended Singer's work by applying digital theory to the design of the input-shaping filter. Brett R. Murphy and Ichiro Watanabe, Digital Shaping Filters for Reducing Machine Vibration, IEEE Transactions on Robotics and Automation, vol. 8, no. 2, pp. 285-289 (April 1992); see also J. T. Feddema et al., Methods for Controlling a Two-Link Flexible Arm, Proceedings of the Fourth Topical Meeting on Robotics and Remote Systems, Albuquerque, N.Mex. (February 24-28, 1991)!.
Auernig and Troger consider time optimal payload maneuvers of a gantry-style crane undergoing trolley translation and load-line length change. J. W. Auernig and H. Troger, Time Optimal Control of Overhead Cranes with Hoisting of the Load, Automatica, vol. 23, no. 4, pp. 437-447 (1987).! The coupled, nonlinear equations of motion and adjoint equations, obtained from the application of Pontryagin's maximum principle, are solved analytically for the cases of constant and variable hoisting speeds. In both cases, the maneuvers are developed such that the payload is residual oscillation free. Moustafa and Ebeid demonstrate a state-feedback controller for damping load sway for a gantry-style crane configured to move along two orthogonal directions in the horizontal plane. Kamal A. F. Moustafa and A. M. Ebeid, Nonlinear Modeling and Control of Overhead Crane Load Sway, Journal of Dynamic Systems, Measurement, and Control, vol. 110, pp. 266-271 (1988).! This work is expanded on by Ebeid et al. to incorporate actuator dynamics into the crane model. A. M. Ebeid, Kamal A. F. Moustafa, and H. E. Emara-Shabaik, Electromechanical Modeling of Overhead Cranes, International J. of Systems Science, Vol. 23, No. 12, pp. 2155-2169 (1992).! Fliess et al. investigate a feedback linearizing controller for a one-dimensional gantry-style crane. M. Fliess, J. Levine, and P. Rouchon, A Simplified Approach of Crane Control Via a Generalized State-Space Model, IEEE Proceedings of the 30th Conference on Decision and Control, Brighton, England, pp. 736-741 (1991).! Trolley traversal and load-line length changes are considered. Simulation results indicate the ability of the closed-loop controller to control load sway for relatively-slow maneuvers. Nguyen examines this same system where simulation and experimental results of a nonlinear state-feedback controller are used. H. T. Nguyen, State-Variable Feedback Controller for an Overhead Crane, Journal of Electrical and Electronics Engineering, Australia, Vol. 14, No. 2, pp. 75-84 (June 1994).! Small motions are assumed about a specified operating point, which allows for decoupled equations of motion and decoupled controller design.
Sakawa and Nakazumi Y. Sakawa and A. Nakazumi, Modeling and Control of a Rotary Crane, Journal of Dynamic Systems, Measurement, and Control, vol. 107, pp. 200-206 (1988).! investigate a rotary crane undergoing hub and boom rotation and load hoisting using a combined open and closed-loop approach. The open-loop input to the crane is designed based on a postulated set of functions such that the sway motion of the load is excited minimally. The closed-loop controller is then switched on when the maneuver is near the end, providing significant sway damping. Vaha et al. generate suboptimal, minimum time inputs for a rotary crane P. Vaha, S. Pieska, and E. Timonen, Robotization of an Offshore Container Crane, Robots: Coming of Age, Proceedings of the 19th ISIR (International Symposium and Exposition on Robots), pp. 637-648 (1988).!. Tracking is achieved via a state feedback control law. Radial sway due to centripetal acceleration of the payload, however, is not compensated. Souissi and Koivo R. Souissi and A. J. Koivo, Modeling and Control of a Rotary Crane for Swing-Free Transport of Payloads, The First IEEE Conference on Control Applications, Dayton, Ohio, pp. 782-787 (1992).! consider a rotary crane undergoing a boom-rotation-boom maneuver using a proportional-integral-derivative controller similar to Fliess et al. M. Fliess, J. Levine, and P. Rouchon, A Simplified Approach of Crane Control Via a Generalized State-Space Model, IEEE Proceedings of the 30th Conference on Decision and Control, Brighton, England, pp. 736-741 (1991).!. The simulation model considers both radial and tangential payload sway, however, the control strategy used results in residual load oscillation.
Despite the prodigious amount of swing-free crane systems of which these references are representative, a practical system that is capable of significantly eliminating payload swing for a rotary-style crane has not been realized until the present invention. The swing-free operator control system and method described herein controls residual oscillation of suspended payloads on a rotary-style crane, which exhibit multiple degrees-of-freedom sway. (Gantry-style cranes exhibit a one degree-of-freedom sway (one direction).) While most operators are very experienced in crane maneuvers, an appropriately-designed controller as in the present invention allows even an inexperienced operator to perform swing-free motions using an operator input or speed control device, such as a button box or a joystick.